Mass exchange in the dialyzer has both a convective component and a diffusive component. In diffusive mass exchange, the mass transfer per unit of time for the respective substance through the membrane is proportional to the concentration gradient between the blood and the dialysis fluid. In convective mass transport, the mass transfer depends on the quantity of filtrate, because the concentration of filterable substances is the same in both the blood and the filtrate. See, Hans Eduard Franz, Blutreinigungsverfahren [Blood Purification Method], pp. 11-13 (Georg Thieme Verlag Stuttgart, New York 1990).
Since the concentration gradient is reduced continuously during a dialysis treatment, no fixed numerical value can be given for the quantity of substance exchanged per unit of time. Clearance is a measured quantity for the efficiency of a dialyzer and is independent of the concentration. The clearance of a substance is the component of the total flow through the dialyzer which has been freed completely of the substance in question.
Dialysance is another term for determining the efficiency of a dialyzer, with the concentration of the substance in the dialysis fluid also being taken into account.
The following is obtained for determination of the dialysance, D, or clearance, K, for a given substance such as sodium.
Dialysance D is equal to the ratio of the mass transport of the respective substance Qb (cbi−cbo) on the blood side, to the difference between the concentrations of the substance in the blood and the dialysis fluid at the respective inlets of the dialyzer (cbi−cdi).                     D        =                  Qe          ⁢                                           ⁢                                    (                              cbi                -                cbo                            )                                      cbi              -              cdi                                                          (        1        )            For mass balance reasons, it holds that:Qe·(cbi−cbo)=−Qd·(cdi−cdo)  (2)It follows from (1) and (2) for the dialysance on the dialysate side:                     D        =                              -            Qd                    ⁢                                           ⁢                                    (                              cdi                -                cdo                            )                                      cbi              -              cdi                                                          (        3        )            where in equations (1) through (3):
Qe =effective blood flow;Qd =dialysis fluid flow rate;cb =concentration of the substance in the solution volume of the blood;cd =concentration of the substance in the dialysis fluid;i =inlet of the dialyzer; ando =outlet of the dialyzer.
The effective blood flow is the flow of the blood component in which the substances participating in the dialyzer metabolism are dissolved, i.e., it is based on the complete (aqueous) solution volume for the respective substance. This may be the plasma water flow or the blood water flow, depending on the substance.
For the case of a specific metabolic excretion product such as urea, cdi is zero, because this substance should not be present in the fresh dialysis fluid when properly used. Otherwise, one would no longer speak of the dialysance D of this substance, but rather the clearance C of this metabolic product.
German Patent No. 39 38 662 describes a method of in vivo determination of parameters of hemodialysis, in particular of the dialysance, where the dialysate-electrolyte transfer is measured at two different inlet dialysate concentrations. On the assumption that the blood inlet concentration is constant, the dialysance is determined according to the known method by determining the difference between the differences in the dialysis fluid ion concentration at the inlet and outlet sides of the dialyzer at the time of the first and second measurements, dividing this by the difference between the dialysis fluid ion concentration at the inlet side at the time of the first and second measurements, and multiplying this by the dialysis fluid flow rate.
In this method, the relatively long measurement time has proven to be a disadvantage for monitoring the course of dialysance over time during the dialysis treatment. This long measurement time is due to the fact that after the new inlet concentration of the dialysis fluid is set, a steady state must first be established at the outlet of the dialyzer before the measured value can be recorded. As a result, a certain period of time must elapse before a jump in conductivity at the dialyzer inlet leads to stable conditions at the dialyzer outlet.
German Patent No. 197 39 100 describes a method of determining the maximum dialysance during a dialysis treatment. In this method, the dialysis fluid inlet concentration of a certain substance in the dialysis fluid is determined upstream from the dialysis fluid chamber of the dialyzer, the outlet concentration of the respective substance in the dialysis fluid is determined downstream from the dialysis fluid chamber, and the inlet concentration of the substance in the blood stream is determined upstream from the blood chamber of the dialyzer. The maximum dialysance is determined from the dialysis fluid inlet and outlet concentrations, the blood inlet concentration, the blood flow through the blood chamber and the dialysis fluid flow rate through the dialysis fluid chamber. One disadvantage of this method is that it allows a determination of only the maximum dialysance, but not of the dialysance for any desired dialysis fluid or blood flow rate.